演講訊息 TALKS

Abstract: In this talk, we discuss some properties of the quantum Zakharov system. First, we talk about the semi-classical limit of the QZ system which is the classical Zakharov system as the quantum parameter goes to zero. One of the difficulties of the convergence is that for the same initial data the solutions of the two systems lie in spaces with different regularities. Thus we need to measure the discrepancy of the solutions to the two systems under a norm with lower regularity. We improve the known result. Then we will discuss the existence and stability of the standing waves of the QZ system. There are several ways to ensure the existence of the ground states. Two ways are based on the minimization method with concentration compactness and with Lagrange multiplier, while the other one is a perturbation of the ground state of the cubic nonlinear Schr\"odinger equation. For the 1D case we can prove that the standing wave is of orbital stability.